Final answer:
Slant asymptotes of rational functions can be found by dividing the numerator by the denominator if its degree is one more than the denominator. The quotient, excluding the remainder, gives the asymptote's equation. Calculators like the TI-83 series can also be used to find slant asymptotes.
Step-by-step explanation:
Finding Slant Asymptotes of Rational Functions
To find the slant asymptotes of rational functions, you need to perform a few steps, which vary depending on the method you choose. For a manual step-by-step solution (Solution A), you would typically divide the polynomial in the numerator by the polynomial in the denominator using either long division or synthetic division if the degree of the numerator is exactly one more than the degree of the denominator. After performing the division, the quotient (ignoring the remainder) gives you the equation of the slant asymptote.
Alternatively, for using a calculator like the TI-83, 83+, or 84 (Solution B), you use the calculator's function to perform polynomial division or to graph the function and estimate the asymptote.
Remember that slant or oblique asymptotes occur when the degree of the numerator is one higher than the degree of the denominator in a rational function. If the degrees are equal, the horizontal asymptote is found by the ratio of the leading coefficients instead.